Horizontal eddy energy flux in the worldoceans diagnosed from altimetry dataChi Xu1, Xiao-Dong Shang1 & Rui Xin Huang2

1State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences,Guangzhou, China, 510301, 2Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA.

During the propagation of coherent mesoscale eddies, they directly or indirectly induce many effects andinteractions at different scales, implying eddies are actually serving as a kind of energy carrier or energysource for these eddy-related dynamic processes. To quantify this dynamically significant energy flow, themulti-year averaged horizontal eddy energy fluxes (EEFs) were estimated by using satellite altimetry dataand a two-layer model based on hydrographic climatology. There is a strong net westward transport of eddyenergy estimated at the mean value of ,13.3 GW north of 56N and ,14.6 GW at the band 56S , 446S in theSouthern Hemisphere. However, poleward of 446S east-propagating eddies carry their energy eastward withan averaged net flux of ,3.2 GW. If confirmed, it would signify that geostrophic eddies not only contain themost of oceanic kinetic energy (KE), but also carry and spread a significant amount of energy with them.

Starting from the first international program, Mid-Ocean Dynamics Experiment and POLYMODE, aimed atobserving mesoscale oceanic eddies1 in 1970s, many programs, including early satellite altimetry missionssuch as SEASAT (1978) and GEOSAT (1986–1989) and the more recent altimetry missions Jason-2 and

Envisat, demonstrate that the sea surface height (SSH) fields are full of mesoscale features2,3. Nearly synopticglobal pictures of the eddy kinetic energy (EKE) distribution are now available from these advanced satellitealtimetry missions4–6. Simple scale analysis7 and altimetry data analysis8, Plate 6 clearly show that EKE is two ordersof magnitude larger than the mean flow KE. Ferrari and Wunsch9 also concluded that ‘‘Oceanic KE is dominatedby the geostrophic eddy field’’.

In addition, mesoscale eddies are the most significant and energetic component of ocean general circulation.They induce transport of heat, salt, carbon, and nutrients and interact with many other dynamic components atdifferent spatial/temporal scales, such as atmospheric forcing10, mean flow11 and internal gravity waves12. Theyexert influence on inertial oscillations13 and diapycnal mixing14. Moreover, the influence of eddies or isolatedvortices can penetrate into the deep circulation15–17.

Most mesoscale eddies move westward in basins with meridional boundaries, carrying energy westward2,3.However, up till now the quantified horizontal energy flux carried by eddies in the world oceans remains unclear.Because this is a critically important component of the global energy budget, a clear dynamical picture and adetailed balance are most desirable. Thus in this paper the eddy-related mechanical energy transport, includingpotential and kinetic energy (KE), was examined based on the previously published method18.

ResultsThe eddy detection and auto-tracking (see Methods) based on weekly TOPEX/ERS merged sea surface heightanomaly (SSHA) data over the period 1993 , 2010 were firstly conducted. Approximately 403,500 eddies wereidentified and the number of long-lived cyclonic (anticyclonic) eddies with lifetime $ 4 weeks were 72341(67506); thus, 34.7% of the observed eddies were long-lived. As the derived eddy propagating speeds are ableto significantly influence the final analysis, the results were compared with those derived from Chelton and Schlaxdataset (http://cioss.coas.oregonstate.edu/eddies/, CS hereafter). As shown in Fig. 1, the results agree with theirsin latitudinal variations of both zonal averaged westward and zonal averaged northward propagating speeds. Amap of the average values of the advective nonlinearity parameter defined by the maximum rotational currentspeed over the propagation speed of the eddy were also shown in Fig. 2 because strong nonlinearity means theenergy will not radiate away at different scales but concentrate within the eddy19.

Secondly, the eddy energy and associated energy source/sink were estimated by assuming that the water-column-integrated eddy kinetic energy (EKE) is equally partitioned between the barotropic mode and the firstbaroclinic mode and by using a two-layer model with equivalent interface depth inferred from a continuously

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PHYSICAL OCEANOGRAPHY

Received12 June 2013

Accepted21 May 2014

Published17 June 2014

Correspondence andrequests for materials

should be addressed toX.-D.S. (xdshang@

scsio.ac.cn)

SCIENTIFIC REPORTS | 4 : 5316 | DOI: 10.1038/srep05316 1

stratified model (see Method). The total amount of EKE is estimatedat 0.96 EJ (1 EJ 5 1018 J); the global amount of eddy available grav-itational potential energy (EAGPE) is 1.63 EJ. The global distri-bution of eddy energy is shown in Fig. 3. It is found that theeastern part of the basin and the ocean interiors near the equatorialband (except the region where tropical instability waves exist) arecharacterized by the lower eddy energy, typically below the level of103 J/m2. The western part of basin, in particular the western bound-ary currents (WBCs, hereafter) and their extensions and the assoc-iated recirculation regimes, are characterized by rather high eddyenergy (on the order of 104–105 J/m2). Another outstanding featureis the high eddy energy, both EKE and EAGPE, associated with theAntarctic Circumpolar Current (ACC). These regions of high eddyenergy are associated with energetic mesoscale variability due to

strong baroclinic instability, and barotropic instability may also con-tribute to these regions of high eddy energy20.

A map of eddy energy sources and sinks is shown in Fig. 4 (thecolor bar is chosen for best visualization). This map is rather similarto Figure 3 in ref. 21. Overall, dissipation of eddy energy is moredominating within the western boundary regions. Inferring frommaps of mean eddy-energy generation rates and dissipation rates(Supplementary Fig. S1), intense eddy-energy dissipations and gen-erations also occur in the ocean interior, in particular near the intensecurrents and the associated recirculation regimes. It means WBCs arealso able to serve as a significant source of eddy energy. Based on thisframework and the updated eddy searching scheme, the globallyintegrated eddy energy generation rates are estimated at 0.38 TWin EKE and 0.60 TW in EAGPE, with the total energy generation rate

Figure 1 | The latitudinal profiles of the global zonal average of the westward (a), (c) and northward (b), (d) propagation speeds of cyclonic (a), (b) andanticyclonic (c), (d) eddies with lifetimes larger than 4 weeks, accumulated over 18 years. Results from our analysis are depicted by black solid lines

with gray shading to indicate the interquartile range of the distribution of the eddy speeds in each 1u latitude band; while black dotted lines are

based on the analysis of CS dataset. The gray solid lines in panels a & c are the latitudinal profile of the zonally averaged westward phase speeds of long

baroclinic Rossby waves. MATLAB R2011a (http://www.mathworks.com/) was used to create the figure.

Figure 2 | The averaged values of U/c, where U is the rotational speed of an eddy and c is its translation speed at that moment. The rotational

speed is defined here by the maximum of the averaged values of the geostrophic speeds around each closed SSHA contours of an eddy. The black thin line

indicates the 200-m isobath. MATLAB R2011a (http://www.mathworks.com/) with M_Map (a mapping package, http://www.eos.ubc.ca/,rich/

map.html) was used to create the map.

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SCIENTIFIC REPORTS | 4 : 5316 | DOI: 10.1038/srep05316 2

estimated at 0.98 TW. Both the volume of eddy energy and its gen-eration rates are much larger than the value reported in the previousstudy. A comparison with estimates based on the cube92 version ofthe CS510 runs of the ECCO2 (Estimating the Circulation andClimate of the Ocean, phase II) and a discussion about the differencebetween this new estimate and other published results are included inthe Supplementary Information.

Next step was to examine multi-year averaged horizontal eddyenergy fluxes (EEFs, here after). With eddy energy and trajectorycalculated, the zonal and meridional energy fluxes associated withmoving eddies were calculated accordingly, Fig. 5.

Within the subtropical band, both cyclonic and anticycloniceddies transport energy westward. Individual eddies are able to carrya large amount of energy, and the multi-year averaged EEF carried bythese eddies can be as high as ,80 MW/degree westward. Due to thecombination of high eddy concentration and high translation speed(as implicated by the formula of phase speed for the baroclinic first-mode Rossby waves), the westward EEF in the subtropical countercurrent around 20uN in the Pacific and in the subtropical gyres of theSouthern Hemisphere around 25uS reach relatively high values.Cyclones and anticyclones give comparative contributions, exceptoff the west coasts of Australia where EEF is dominated by cycloniceddies2,22.

Additionally, high EEF in WBCs and the recirculation systems aredue to the strong unstable and meandering flows that give rise to

shed-off eddies propagating within the recirculation systems. In theNorthern Hemisphere around 35uN, especially on the equatorwardside of the eastward currents like the Gulf Stream, the westward EEFcarried by cyclones is able to reach the level of ,80 MW/degree(Fig. 5a). The circumstance on the equatorward side of theKuroshio around 34uN is similar, but the corresponding EEF is muchweaker. Likewise, the predominant energy flux induced by anticy-clones appears on the poleward side of these eastward currents, butthe regions are much narrower (Fig. 5c). This is consistent with thegeographical distribution of eddy polarity discussed by ref. 2. In theSouthern Hemisphere, along east coasts of continents strong west-ward components of EEF are associated with the strong WBCs, suchas the Agulhas Current, the East Australian Current and the BrazilCurrent. Eddies in the Benguela Current contribute to another localhigh value of westward EEF.

Eastward EEF appears primarily in the ACC and other strongeastward boundary currents, such as the Kuroshio Extension at38uN band, the Gulf Stream Extension at 40uN band and theAgulhas Return Current. The existence of eastward moving eddiesmay be explained by the fact that they are advected by mean flow23.The zonally averaged zonal EEF changes sign around 44uS (Fig. 6a).In particular, the latitudinal band of 56uS to 61uS has no zonalboundary, where eddy activity is very strong, and the associatedeastward EEF is high. Within the core of ACC, the eastward EEF(including ,50 MW/degree contribution from cyclones and

Figure 3 | Horizontal distribution of mean EKE (a) and mean EAGPE (b) in log10 form (of unit J/m2). The black thin line indicates the 200-m isobath.

MATLAB R2011a (http://www.mathworks.com/) with M_Map (a mapping package, http://www.eos.ubc.ca/,rich/map.html) was used to create the map.

Figure 4 | The patterns of sources and sinks of eddy (with lifetimes no less than 2 weeks) energy (unit: mW/m2) derived from generation ratesminus dissipation rates in 16 3 16 boxes. The interval among contours is 0.2 mW/m2 and the black thin line indicates the 200-m isobath. MATLAB

R2011a (http://www.mathworks.com/) with M_Map (a mapping package, http://www.eos.ubc.ca/,rich/map.html) was used to create the map.

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SCIENTIFIC REPORTS | 4 : 5316 | DOI: 10.1038/srep05316 3

,50 MW/degree contribution from anticyclones) are on the order of,100 MW/degree, with the highest value exceeding ,200 MW/degree.

Comparing with the zonal component, the meridional componentof EEF does not have a clear pattern of sign in most basin interiors(Fig. 5b & 5d). Even in the subtropical bands full of eddies, thereseems no well-defined sign of meridional energy transport. It seemsthat at a given location EKE/EAGPE transport can be either pole-ward or equatorward, appearing at different times. However, eddiesgenerated in meridional boundary currents, specially the LeeuwinCurrent, the Agulhas Current and the Benguela Current originatedfrom the Agulhas Retroflection, have their preferable meridionaldeflection according to their polarity2,22. Hence, there are dominantdirections of meridional EKE/EAGPE transport. For example, thepoleward EEF for Leeuwin Current cyclones is ,20 MW/degree, thesouthward energy flux of cyclones in the Agulhas Current is,35 MW/degree, and the northward flux for Agulhas anticyclonicrings pinching off the Agulhas Retroflection and joining theBenguela Current is ,40 MW/degree. High values of meridional

components of mean EEF for both cyclonic and anticyclonic eddies,are mainly concentrated in the vicinity of the major surface currentsystems, especially the ACC. The multi-year averaged meridionalcomponents of EEF in the ACC band are on the order of 25 MW/degree. In the ACC band meridional energy flux associated withcyclones are equatorward while those associated with anticyclonesare poleward. It is opposite to what occurs north of ACC2,22. Suchbehavior is associated with the shedding process of an eastward jet,and it may be explained by the vorticity balance analysis24.

To illustrate an overall estimate of the strength of the zonal energytransport due to eddies, the world oceans were separated into 5 zonalbands according to different eddy-concentrated regions and the mer-idionally-integrated zonal EEFs are shown (Fig. 6b). Nine cases ofcalculation based on different scales of spatial filter (with half-powercutoffs at 5u, 10u and 15u) and different thresholds of closed contourof SSHA (at 64 cm, 65 cm and 66 cm) are also considered here foraccuracy. Overall, there is nearly ,13.3 GW of westward eddyenergy transport in the Northern Hemisphere and ,14.6 GW ofwestward eddy energy transport in the 5u , 44uS band in the

Figure 5 | The multi-years averaged zonal (a), (c) and meridional (b), (d) components of eddy-energy flux of cyclonic eddies (a), (b) and anticycloniceddies (c), (d) with lifetimes larger than 4 weeks, in unit of MW/degree. The black thin line indicates the 200-m isobath. MATLAB R2011a

(http://www.mathworks.com/) with M_Map (a mapping package, http://www.eos.ubc.ca/,rich/map.html) was used to create the map.

Figure 6 | Zonal and meridional distributions of zonal EEF averaged from nine cases of calculation based on different scales of spatial filter anddifferent thresholds of closed contour of SSHA. (a), the mean zonal EEF in each 1u latitudinal band (in unit of MW/degree) with shading indicates the

standard deviation over the nine cases. (b), The meridionally-integrated zonal EEF of 5 latitudinal bands (in unit of GW) with shading indicates the

standard deviation over the nine cases. The numbers in the legend indicate the mean values of each solid line. MATLAB R2009a (http://www.mathworks.

com/) was used to create the figure.

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SCIENTIFIC REPORTS | 4 : 5316 | DOI: 10.1038/srep05316 4

Southern Hemisphere. In addition, there is ,3.2 GW mean eastwardeddy energy transport in the unique ACC band.

DiscussionThe energy pathways (not cascade, but spatial energy flow) related tothe nonlinear mesoscale eddies, the most energetic component ofmesoscale variability, can be understood by connecting the energytransports with their sources and sinks. As illustrated in theSupplementary Fig. S2, the EEF vectors among different regimes oftheir horizontal divergence denote the energy transports betweenthese sources and sinks on average. When westward EEFs at mid-latitudes arrive in the western boundaries, they mainly convergethere, implying eddy energy dissipations dominate in the westernboundaries. However, the eddy energy that dissipates here does notnecessarily come from where the eddies are generated because eddy-mean flow interaction occurs everywhere during their propagation25.

The estimates of multi-year averaged EKE/EAGPE fluxes inducedby long-lived mesoscale eddies indicate that high flux of EKE/EAGPE is compatible with the locations of energetic regions ofmesoscale variability. Meanwhile, it is found that the multi-yearaveraged EEFs result from those eddies with lifetimes no less than17 weeks strongly contribute to the eddy energy transports in theinteriors of ocean basins (Supplementary Fig. S3). More significant isthat EEFs are comparable with the mean energy input from the windinto the geostrophic currents in each 1u 3 1u bin, implying most ofthe eddy energy, originated from potential energy of large-scale meanflow generated by the wind, is carried away by mesoscale eddiesrather than dissipated locally. Thus, geostrophic eddies not onlycontain the most of ocean KE, but also carry and spread a significantamount of energy with them. It is noted that the EEFs estimated inthis study come from mesoscale coherent vortexes, whereas a signifi-cant part of energy flux due to other types of eddying motions is notincluded in this estimation. Both mean advection and wind can affectthe direction of EEFs, but how these effects modify EEFs is beyondthe scope of this study.

There are several uncertainties in the present estimations. First,the criterion of 65 cm closed contour of SSHA chosen for eddyidentification may underestimate the eddy area. However, the altera-tion of this standard does not seem to substantially affect the results.Second, a 2-dimension spatial high-pass filtering with critical half-power cutoffs was chosen and the estimates are more sensitive to thescales of spatial filter rather than the thresholds of closed contour ofSSHA that were chosen in the eddy detection. Here we show spatialpatterns of eddy energy, sources and sinks, and associated EEFs whenspatial filter with half-power cutoffs at 10u of longitude and 10u oflatitude is applied, because we confirmed that most of the eddysignals are retained from the spectrum analysis and the animationsof filtered SSHA field (both not shown). Third, animation of thefiltered SSHA field shows that the temporarily distorted eddies invol-ving with eddy-flow interaction or eddy-eddy interaction in thestrong currents have rather complex movements compared withthe isolated eddies with persistent and coherent structures in weakflow. Thus, tracking these eddies in the ACC and WBC extensionsare rather difficult, and the error of tracking results there may berelatively large. Fourth, the results reported in this paper are limitedby the current state of art in this field. For example, the verticalstructure of eddies is unclear. In this study, because eddies maypenetrate quite deep15–17,26–28 we use the interface depth inferred froman equivalent 2-layer model (Fig. 2 in ref. 18), which is deeper thanthe depth of main thermocline. The calculation is based on a workingassumption that the water-column-integrated EKE is equally parti-cipated between the barotropic mode and the first baroclinic mode,and energy in higher baroclinic modes are not considered herealthough they are typically concentrated in the upper ocean mixedlayer29,30. There is currently, however, no better understanding ofsuch partition in the ocean based on observation. Thus, we adapted

this seemingly crude assumption. Whether these assumptions areappropriate are left for further studies based on in situ observationsand eddy-resolving numerical models.

Despite the potential shortcoming in these estimates, we hope thatthe spatial patterns of EEFs, the latitudinal variations of EEF com-ponents and other aspects of our results are useful for understandinghow mesoscale eddies are transferring energy across the oceanbasins.

MethodsThe dataset. The weekly TOPEX/ERS merged data distributed by ArchivingValidation and Interpretation of Satellite Data in Oceanography (AVISO) over period1993 , 2010 were used in the analysis. They are referred to as the ‘‘Reference’’ Seriesand cover the latitude band from 60uS to 60uN on a Mercator grid with resolution of1/3u. Through interpolation, a global dataset with uniform resolution of 1/4u by 1/4ugrid was obtained. As errors of altimetry data are larger near continental boundaries,the sea surface height anomaly (SSHA) data over regimes with depth shallower than200 meters were abandoned. Many issues related to the quality and utility of thisdataset have been discussed in previous studies, e.g. refs. 2 & 3.

The stratification was calculated based on the WOA01 annual mean climatology oftemperature and salinity31. The vertical profiles of T and S at each 1u 3 1u grid pointwere linearly interpolated to a vertically uniform grid of 50 meter interval. Thebuoyancy frequencies were calculated by using the standard Matlab subroutine:seawater (http://www.cmar.csiro.au/datacentre/ext_docs/seawater.htm).

Mesoscale eddy identification and tracking. A two-dimensional Gaussian high-passfilter was applied to the SSHA fields to identify eddy-like signals with space scales of100 km. The filter was designed as follows:

K(x,y)~e{

(x{x0 )2z(y{y0 )2

2k02 , ð1Þ

where K is the filter transfer function and k0 is the spatial cut-off wavelength. Here k0

was chosen to insure that spatial filtering has half-power cutoffs at 10u of longitudeand 10u of latitude; this choice of filtering retains most of mesoscale signals.

Eddy identification. Three criteria were applied to identify eddies.

1) A closed contour of SSHA $65 cm. The 65 cm threshold was chosen so thateddies in the relatively low-energetic and more stable regions, such as the NorthPacific Subtropical Countercurrent region, are able to be detected. These eddieshave shapes similar to the Gaussian profile. However closed contours in theenergetic WBCs will result in larger eddy area due to higher amplitude of SSHA,and the shapes of these eddies are close to meanders. These meanders are thedominating mesoscale features drawing energy from the unstable mean flow.

2) The zonal and longitudinal spreads of the area enclosed by SSHA contour areboth at least 0.5u.

3) There is at least one SSHA maximum (or minimum) in the enclosed area. Tofind the location of the eddy and minimize the errors, the central location of theeddy was defined as the midpoint between the centroid of the area within theclosed SSHA contour and the location of the SSHA extremum. As f approacheszero near the equator, eddy calculation in this study was limited to 5u off theequator.

Eddies auto-tracking. To track nonlinear eddies at consecutive time steps, a domainas ref. 2’s choice was searched. The smallest domain is a circle with radius of 150 kmcentralized at the center of an eddy at previous time step. A critical distance dc 5

1.75(cR ?Dt), where cR is the local long baroclinic Rossby wave phase speed32 andDt 5

7 days is the time step, was used. If dc is larger than 150 km, the domain changes intoan ellipse with western extremum of the distance dc. If an eddy center at next time stepis located within the searched domain derived from an eddy at the previous time step,these two eddies are considered as the same eddy at these two time steps. To avoidcounting two eddies with quite different sizes at neighbor steps as one eddy, theamplitude and area of the eddy in tracking must fall within 0.25 and 2.5 times those ofthe reference eddy. As ref. 2 pointed out, searching ahead more than one time step is‘‘unsuccessful’’; thus, one time-step searching was used here.

EEF estimation. Eddies in the ocean are able to be classified according to their verticalstructures. A common practice is based on the normal mode decomposition, i.e.,observed eddies are decomposed into the barotropic mode and a seires of baroclinicmodes. A critical issue is the partition of eddy energy among these possible modes.Due to the complicated nature of eddy dynamics, such a partition may depend on thetime and geographic location, and it is a current research frontier.

As a working assumption, the simplified approach used in the previous study18 isadapted in this study. Accordingly, it is assumed that the water-column-integratedkinetic energy is equally partitioned between the barotropic mode and the first bar-oclinic mode. Such an assumption is consistent with conclusions in previous studiesthat most part of KE in the upper ocean is contained in the first baroclinic mode33 andthe KE of an entire water column at periods beyond 1 day is roughly equally par-titioned between the barotropic mode and the first baroclinic mode34.

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SCIENTIFIC REPORTS | 4 : 5316 | DOI: 10.1038/srep05316 5

Technically, following ref. 35, an equivalent two-layer model inferred from acontinuously stratified model was used, and the interfacial depth by solving the eigenvalue problem was shown in Fig. 2a of Ref. 18. The upper layer thickness is mostlydeeper than 500 meters poleward of 40u. Within the central latitude band of ACC,especially south of 45uS, the equivalent interface depth is on the order of 1000 m.These features are respectively consistent with the climatological data analysis26 andthe model results in the subpolar gyre27 and in the ACC band28. Other details of such atwo-layer model are referred to ref. 18.

The total geostrophic kinetic energy of each eddy is

EKE~Xn

i~1

1{að Þ2rAi(g+gi=f )2H1,iHi=H2,i: ð2Þ

a~ 1z

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiH2,i

H1,i

1{cc

s !{1

, ð3Þ

where a[½0,1� means the fraction of the barotropic components of SSHA signals;�r^1030 kg=m3 is the reference density; H1,i, H2,i, Hi 5 H1,i 1 H2,i are the upper-layer, lower-layer, and total thickness, respectively, at gridpoint i; c is the percentage ofbarotropic KE in the total EKE and assumed as 0.5; g is the gravity acceleration; gi isSSHA at gridpoint i; Ai is area of gridbox i; n is the number of the gridpoints enclosedin the eddy boundary; f 5 2Vsinh is the Coriolis parameter; V is the earth rotationrate; and h is the latitude.

The corresponding formula for the EAGPE is

EAGPE~Xn

i~1

1{að Þ2rggi2 Hi=H2,ið Þ2Ai=2ei, ð4Þ

where ei~Dri=�r and Dri is the density difference between the two layers at gridpointi. How to calculate the estimates of eddy-energy dissipation/generation rates is alsoreferred to Ref. 18.

Before the IEEF is calculated, it is emphasized that the coherent mesoscale eddiesidentified and tracked in this paper are treated as non-dispersive structures accordingto Ref. 19’s analysis. Thus, the phase and group velocities are not distinguished as theyare for linear Rossby waves. Then, the calculation is as follows. Suppose that n eddieshave passed across a meridional 1-degree line segment in the 18 years. The zonalcomponent of the mean EEF vector there is computed as

EEFzonal~

Pni~1

(EiDxiDli

)

T, ð5Þ

where Ei is the total eddy energy (EKE plus EAGPE) of eddy i, Dli is the distance thateddy i traveled across the line segment during the time step, and Dxi is the projection

of the trajectory onto the direction-axis (so that EDxDl

is the zonal component of

energy flux for eddy i, and T 5 18 years. An analogous calculation is carried out foreach zonal 1-degree line segment.

1. Gould, W. J., Schmitz Jr, W. J. & Wunsch, C. Preliminary field results for a Mid-Ocean Dynamics Experiment (MODE-0). Deep. Sea. Res. 21, 911–931 (1974).

2. Chelton, D. B., Schlax, M. G. & Samelson, R. M. Global observations of nonlinearmesoscale eddies. Prog. Oceanogr. 91, 167–216 (2011).

3. Chelton, D. B., Schlax, M. G., Samelson, R. M. & de Szoeke, R. A. Globalobservations of large oceanic eddies. Geophys. Res. Lett. 34, L15606 (2007).

4. Stammer, D. Global characteristics of ocean variability estimated from regionalTOPEX/POSEIDON altimeter measurements. J. Phys. Oceanogr. 27, 1743–1769(1997).

5. Ducet, N., Le Traon, P. Y. & Reverdin, G. Global high-resolution mapping ofocean circulation from TOPEX/Poseidon and ERS-1 and -2. J. Geophys. Res. 105,19,477–19,498 (2000).

6. Pascual, A., Faugere, Y., Larnicol, G. & Le Traon, P. Y. Improved description of theocean mesoscale variability by combining four satellite altimeters. Geophys. Res.Lett. 33, L02611 (2006).

7. Gill, A. E., Green, J. S. A. & Simmons, A. J. Energy partition in the large-scale oceancirculation and the production of mid-ocean eddies. Deep. Sea. Res. 21, 499–528(1974).

8. Wunsch, C. The past and future ocean circulation from a contemporaryperspective, in Ocean Circulation: Mechanisms and Impacts—Past and FutureChanges of Meridional Overturning. Geophys. Monogr. Ser. 173, 53–74 (2007).

9. Ferrari, R. & Wunsch, C. Ocean circulation kinetic energy: reservoirs, sources, andsinks. Annu. Rev. Fluid. Mech. 41, 253–282 (2009).

10. Chow, C. H. & Liu, Q.-Y. Eddy effects on sea surface temperature and sea surfacewind in the continental slope region of the northern South China Sea. Geophys.Res. Lett. 39, L02601 (2012).

11. Waterman, S., Hogg, N. G. & Jayne, S. R. Eddy–Mean Flow Interaction in theKuroshio Extension Region. J. Phys.Oceanogr. 41, 1182–1208 (2011).

12. Polzin, K. L. Mesoscale Eddy–Internal Wave Coupling. Part II: Energetics andResults from PolyMode. J. Phys. Oceanogr. 40, 789–801 (2010).

13. Elipot, S., Lumpkin, R. & Prieto, G. Modification of inertial oscillations by themesoscale eddy field. J. Geophys. Res. 115, C09010 (2010).

14. Saenko, O. A., Zhai, X., Merryfield, W. J. & Lee, W. G. The combined effect oftidally and eddy driven diapycnal mixing on the large-scale circulation. J. Phys.Oceanogr. 42, 526–538 (2012).

15. Dengler, M. et al. Break-up of the Atlantic deep western boundary current intoeddies at 8[deg] S. Nature. 432, 1018–1020 (2004).

16. Lozier, M. S. Deconstructing the Conveyor Belt. Science. 328, 1507–1511 (2010).17. Adams, D. K. et al. Surface-Generated Mesoscale Eddies Transport Deep-Sea

Products from Hydrothermal Vents. Science. 332, 580–583 (2011).18. Xu, C., Shang, X.-D. & Huang, R. X. Estimate of eddy energy generation/

dissipation rate in the world ocean from altimetry data. Ocean. Dynam. 61,525–541 (2011).

19. Early, J. J., Samelson, R. M. & Chelton, D. B. The evolution and propagation ofquasigeostrophic ocean eddies. J. Phys. Oceanogr. 41, 1535–1555 (2011).

20. Weijer, W. et al. Agulhas ring formation as a barotropic instability of theretroflection. Geophys. Res. Lett. 40, 5435–5438 (2013).

21. Zhai, X., Johnson, H. L. & Marshall, D. P. Significant sink of ocean-eddy energynear western boundaries. Nat. Geosci. 3, 608–612 (2010).

22. Morrow, R., Birol,F., Griffin, D. & Sudre, J. Divergent pathways of cyclonic andanti-cyclonic ocean eddies. Geophys. Res. Lett. 31, L24311 (2004).

23. Klocker, A. & Marshall, D. P. Advection of baroclinic eddies by depth-mean flow.Geophys. Res. Lett. In press (2014). DOI: 10.1002/2014GL060001.

24. Cushman-Roisin, B. & Beckers, J. Introduction to Geophysical Fluid Dynamics,Academic Press. 875 pp (2011).

25. Zu, T. et al. Evolution of an anticyclonic eddy southwest of Taiwan. Ocean.Dynam. 63, 519–531 (2013).

26. Tulloch, R., Marshall, J., Hill, C. & Smith, K. S. Scales, Growth Rates, and SpectralFluxes of Baroclinic Instability in the Ocean. J. Phys. Oceanogr. 41, 1057–1076(2011).

27. Zhai, X. & Marshall, D. P. Vertical Eddy Energy Fluxes in the North AtlanticSubtropical and Subpolar gyres. J. Phys. Oceanogr. 43, 95–103 (2013).

28. Petersen, M. R., Willianms, S. J., Maltrud, M. E., Hecht, M. W. & Hamann, B. Athree-dimensional eddy census of a high-resolution global ocean simulation.J. Geophys. Res. 118, 1–16 (2013).

29. Scott, R. B. et al. Total kinetic energy in four global eddying ocean circulationmodels and over 5000 current meter records. Ocean. Modell. 32, 157–169 (2010).

30. Scott, R. B. & Furnival, D. G. Assessment of Traditional and New EigenfunctionBases Applied to Extrapolation of Surface Geostrophic Current Time Series toBelow the Surface in an Idealized Primitive Equation Simulation. J. Phys.Oceanogr. 42, 165–178 (2012).

31. Boyer, T. et al. Objective analyses of annual, seasonal, and monthly temperatureand salinity for the world ocean on a 1/4 degree grid. Int. J. Climatol. 25, 931–945(2004).

32. Chelton, D. B., De Szoeke, R. A. & Schlax, M. G. Geographical variability of the firstbaroclinic Rossby radius of deformation. J. Phys.Oceanogr. 28, 433–460 (1998).

33. Wunsch, C. The vertical partition of oceanic horizontal kinetic energy.J. Phys.Oceanogr. 27, 1770–1794 (1997).

34. Ferrari, R. & Wunsch, C. The distribution of eddy kinetic and potential energies inthe global ocean. Tellus. Ser. A. 60, 92–108 (2010).

35. Flierl, G. R. Models of vertical structure and calibration of 2-layer models. Dynam.Atmos. Oceans. 2, 341–381 (1978).

AcknowledgmentsWe thank Ryo Furue for his extremely careful and constructive comments on themanuscript.This study used altimeter data available by the AVISO Altimetry Operations Center, plushydrographic data World Ocean Atlas 2001 provided by the U.S. National OceanographicData Center. This study is supported by Grants XDA11010202, 2011CB403505,2013CB430303; Projects 41306016, U1033002, 40976021 of NNSFC and LTOZZ1304. TheMATLAB R2009a, R2011a were employed to plot all the figures.

Author contributionsC.X. conducted data analysis. R.X.H. and X.D.S. contributed to design of the study. C.X.,X.D.S. and R.X.H. all contributed to interpretation of the results and writing of themanuscript.

Additional informationSupplementary information accompanies this paper at http://www.nature.com/scientificreports

Competing financial interests: The authors declare no competing financial interests.

How to cite this article: Xu, C., Shang, X.-D. & Huang, R.X. Horizontal eddy energy flux inthe world oceans diagnosed from altimetry data. Sci. Rep. 4, 5316; DOI:10.1038/srep05316(2014).

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